While the two are certainly correlated in exercise, latest studies show that lactic acid is NOT directly responsible - understanding lactic acid's role in muscle physiology can maximize your workouts' effects.
From a NYTimes article (source):
"The understanding now is that muscle cells convert glucose or glycogen to lactic acid. The lactic acid is taken up and used as a fuel by mitochondria, the energy factories in muscle cells.
Mitochondria even have a special transporter protein to move the substance into them, Dr. Brooks found. Intense training makes a difference, he said, because it can make double the mitochondrial mass.
It is clear that the old lactic acid theory cannot explain what is happening to muscles, Dr. Brooks and others said."